Sufficient conditions for the filtration of a stationary processes to be standard

Details Sufficient conditions for the filtration of a stationary processes to be standard Sufficient conditions for the filtration of a stationary processes to be standard

2011-10-25

arxiv.org/abs/1110.5465v1

Mathematics

Probability

Scientific paper

Let $X$ be a stationary process with values in some $\sigma$-finite measured state space $(E,\mathcal{E},\pi)$, indexed by $\Z$. Call $\F^X$ its natural filtration. In \cite{ceillierstationary}, sufficient conditions were given for $\F^X$ to be standard when $E$ is finite. The proof of this result used a coupling of all probabilities on the finite set $E$. In this paper, we construct a coupling of all laws having a density with regard to $\pi$, which is much more involved. Then, we provide sufficient conditions for $\F^X$ to be standard, generalizing those in \cite{ceillierstationary}.

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